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Back to the main valsi listing.
 valsi cnansari type fu'ivla creator krtisfranks time entered Sun Apr 1 05:01:25 2018

Examples

English
Definition #70583 - Preferred 

definition x1 is the mean-value theorem mean/forward-difference-quotient mean of the elements of (multi)set x2 (1-element or 2-element set) under/for function x3.
notes Let the sumti of x3 be a real-valued, univariate function f which is defined and continuous on at least the closed interval [ min(x2), max(x2)] and differentiable on at least the open interval (min(x2), max(x2)), such that the derivative f' is injective. Then x1 = (f')(-1)((f (max(x2)) - f (min(x2)))/(max(x2) - min(x2))) if x2 has cardinality 2; if x2 has cardinality 1, then x1 is equal to the sole element of that set; other repairs may be necessary, depending on f: for example, f = log has x1 = 0 if 0 is an element of x2. If x3 is filled with the monic, single-term polynomial of (integer) degree p such that p > 1, then x1 will be the principal (p-1)th root of the (1/p)-scaled weighted (p,1)-Lehmer mean (cnanlime) of the elements of x2 wherein the weight of the lesser of them is -1 (and the other weight is +1) unless x2 is a singleton (in which case the weights are both +1). Usually, x1 is the value which is guaranteed to exist for appropriate function x2 by the Mean-Value Theorem.
gloss words
created by krtisfranks
vote information 1
time Sun Apr 1 05:59:29 2018

Examples
 Etymology

 krtisfranks {cnano} + {salpo} + {salri} + {dugri}. 
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